Technical and medical endoscopes can be rigid endoscopes containing a lens system, flexible endoscopes containing a flexible image guiding bundle or video endoscopes. Rigid endoscopes are preferred by most physicians because of their optical quality and ease of handling.
Rigid endoscopes have a small diameter of a few millimeters but are often several hundreds of millimeters long. These endoscopes contain an outer tube and an inner tube. The space between the outer tube and inner tube is filled with illumination fibers which guide externally created light inside the cavities such as body cavities. Rigid endoscopes have inside the inner tube an optical system which relays an image created by an objective from the distal tip of the endoscope back to the proximal end of the endoscope. This image relayed to the proximal end can be observed by the operator's eye, or a video camera can capture the image.
First endoscopes with lens systems were simple designs with achromats as relay systems and oculars, plano-convex or bi-convex lenses as field lenses and objective lenses. The number of lenses was limited because the advantage of increasing the number of lenses is offset by the increase of reflections at the glass air surfaces. After the introduction of anti-reflection coatings the number of lenses and therewith the number of relay systems could be increased.
The brightness of modern endoscopes depends on the brightness of the relay system. This brightness is measured by the numerical aperture of the relay system. The numerical aperture is a dimensionless number that characterizes the range of angles over which the system can accept or emit light. By incorporating index of refraction in its definition, numerical aperture has the property that it is constant for a beam as it goes from one material to another provided there is no optical power at the interface.
Almost all endoscopic surgeries are done today using endoscopic cameras at the proximal end of the endoscopes. The physicians and their staff observe the endoscopic procedure on one or more monitors used in the operating room. Such endoscopic cameras have dramatically improved in the last years and exceed the former NTSC standard. Today, digital endoscopic cameras with high definition (HD) resolution are the norm in operating rooms.
Most optical designs of rigid endoscopes were developed twenty and more years ago, and the resolution of these endoscopes does not meet the resolution of modern HD cameras. The resolution of endoscopes is limited by either the diffraction limit represented by the so-called airy disk or by the spot size created by geometric optical aberrations. The airy disk refers to the bright spot in a diffraction pattern resulting from a uniformly-illuminated circular aperture. In an ideal corrected endoscope, the geometric optical aberrations will be optimized so much that the geometrical optical spot size meets roughly the airy disk representing the diffraction limit. Optical aberrations refer to departures of the performance of an optical system from the predictions of paraxial optics. Optical aberrations occur when light from one point of an object does not converge into, or does not diverge from, a single point after transmission through the system.
The diffraction limit of an endoscope depends on the numerical aperture of the relay system. The numerical aperture of the relay system is determined by the type of relay, free lens diameter and the length of the relay system. By manipulating these parameters the diffraction limit of the relay system can be reduced which results in a smaller airy disk and higher numerical aperture. However, the increase of the numerical aperture decreases the depth of field. So every optical system in an endoscope is a compromise between the depth of field and the size of the airy disk.
Endoscopes, like so-called needle scopes, with small outer diameter and therewith small lens diameter have a large diffraction limit. This is why the spot size of the geometrical optical aberrations of such endoscopes can also be larger. Conversely, endoscopes with a larger lens diameter have a lower diffraction limit. For such endoscopes today, the geometric optical aberrations are not corrected to match the diffraction limit.
In an optical design, basic monochromatic and chromatic aberrations of optical systems i.e., distortions in which there is a failure of a lens to focus all colors to the same convergence point, are minimized in a way that the spot size of the geometrical optical aberrations is minimized over the whole field. To achieve this not every component of the optical system needs to be fully optimized. As Ernst Abbe defined for the microscope, some components can be over corrected or under corrected for certain aberrations as long as the over corrected and under corrected aberrations from different components compensate in the whole instrument. To optimize the aberrations of endoscopes, the aberrations of the different components like the ocular, relay and objective systems must also compensate one another.
The five monochromatic aberrations are spherical aberration, coma, astigmatisms, field curvature and distortion. The two chromatic aberrations are axial color and lateral color. Coma, distortion and lateral color are caused by the asymmetry of an optical system or optical component. Correction of spherical aberrations and axial color are correlated. Axial color is the variation of the spherical aberrations for different colors of the visual spectrum.
The correction of aberrations in endoscopes can be shown by the classical Hopkins rod lens system which consists of a number of pairs of rod lenses where each pair is symmetrical to the center of the relay system. These symmetrical relay systems do not contribute to coma, distortion or lateral color of the whole optical system of the endoscope. The rod lenses in these relay system are simple achromatic systems which are designed to limit the effects of chromatic and spherical aberration. Astigmatism and field curvature are not fully corrected or in other terms under corrected. However, the achromatic system corrects the spherical aberrations and axial color. The relay system has the largest numerical aperture of all the components in the endoscope. Residual spherical aberrations and the variation of the spherical aberrations for different colors from the relay system will be dominant. Additionally, these aberrations are multiplied by the number of relay systems.
The ocular is usually a simple achromat. Used with a lower numerical aperture than the relay system, the ocular contributes also to the spherical aberrations and axial color but less than one single rod lens in the relay system. The ocular is unique in the endoscope system because the marker plate sitting in front of the ocular is the only element not seen through the whole optical system of the endoscope. The marker plate is a radial object located at the periphery of the object field of the ocular. Coma in the ocular design makes it impossible to focus on the marker plate. Lateral color causes a colored border of the marker plate. Therefore, the ocular has to be corrected for coma and lateral color for the edge of the field where the marker plate is located.
The objective system of the Hopkins design consists of four components or groups of components which have different functions and different influence on the total correction of the aberrations of the endoscope. At the distal tip is a lens or lens group with extreme high negative refractive power. This lens or lens group with high negative refractive power has an over corrected field curvature which compensates the remaining under corrected field curvature of all the other components of the optical system of the endoscope. A negative lens with extreme high refractive power creates also high distortion. Early Hopkins endoscopes did not correct this distortion. Later, designs reduced or corrected the distortion by introducing a cemented surface in the front lens group. The second group in the Hopkins objective is a prism or prism block which deflects the optical axis of the proximal part of the optical system of the endoscope laterally towards the object field.
On the proximal side of the prism comes first an objective lens or objective lens group followed by one or more field lenses. The objective lens or objective lens group and the field lenses ensure that the chief rays of the off axial object points cross inside the prism. Cemented surfaces within the objective and field lenses have extreme curvatures to create under corrected astigmatism to compensate the accumulated astigmatism of the relay system and ocular. The objective system also compensates the coma and lateral color. However, unlike the astigmatism there is no accumulated coma and lateral color from the relay system or ocular.
Axial and lateral color is normally calculated for three basic wavelengths of the visual spectrum. Achromatic systems correct the focus for two colors, typically close to the edges of the visual spectrum. This common focal length for the two colors for the edge of the spectrum is normally different for the focal length for the center wave length of the visible spectrum. The difference depends on the glass selection. Also, the spherical aberration of an achromatic system varies for different wave lengths. An endoscope corrected for axial and lateral color for three wave lengths still has aberrations for other wavelengths of the visual spectrum called secondary spectrum.
In view of the shortcomings of current endoscope optical systems, especially when used with HD cameras, there is a need for an optical system for endoscopes having low diffraction limit with a correction for the geometrical optical aberrations matching the diffraction limit of the optical system for more than the three basic wavelengths. Such a diffraction limited correction of the aberrations becomes more complicated with brighter optics and larger lens systems.